Research on Rational Number Arithmetic Library in Many-Core Massively Parallel Cluster

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K00168
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: High performance computing
• Research Institution: University of Tsukuba
• Principal Investigator: TAKAHASHI Daisuke 筑波大学, 計算科学研究センター, 教授 (00292714)
• Research Collaborator: SAMUKAWA HIKARU
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 有理数算術演算 / 多倍長整数演算 / モジュラー算術演算 / SIMD化

Outline of Final Research Achievements

We performed vectorization using SIMD instructions in the hierarchy of multiple-precision integer arithmetic. Specifically, we evaluated the performance by speeding up unsigned 64-bit integer division for multiple dividend and divisor using SIMD instructions. Using this method, we proposed a fast calculation method of BBP type formula that calculates a specific digit of mathematical constants. In addition, vectorization with Intel AVX-512 instruction is performed by using reduced-radix representation in multiple-precision integer multiplication. We implemented modular arithmetic to speed up rational arithmetic in a rational arithmetic programming environment.

Free Research Field

高性能計算

Academic Significance and Societal Importance of the Research Achievements

多倍長演算ライブラリとしてGNU Multi-Precision Library（GMP）が知られているが、SIMD命令はほとんど用いられていない。本研究課題では多倍長乗算および複数の被除数と除数に対する符号なし64ビット整数除算をSIMD命令を用いて高速化することができた。多倍長演算は現在公開鍵暗号などで広く用いられており、本研究課題で提案した手法はこれらの高速化に貢献できると期待できる。